Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies

@article{Iglesias2018ShapeAwareMO,
  title={Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies},
  author={Jos{\'e} A. Iglesias and Martin Rumpf and Otmar Scherzer},
  journal={Foundations of Computational Mathematics (New York, N.y.)},
  year={2018},
  volume={18},
  pages={891 - 927}
}
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed… 
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14 Citations
Background Citations
5
Methods Citations
3

14 Citations

Symmetry and scaling limits for matching of implicit surfaces based on thin shell energies
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A novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features and is applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes.
Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework
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This paper relaxes the geodesic boundary constraint using an auxiliary parametrization-blind varifold fidelity metric, which provides the flexibility to deal with simplicial meshes of arbitrary topologies and sampling patterns and makes the algorithm scalable to large meshes.
Geometry Processing with Neural Fields
TLDR
This paper proposes the use of neural fields for geometry processing, and introduces loss functions and architectures to show that some of the most challenging geometry processing tasks, such as deformation and filtering, can be done with neural fields.
Fluid image registration using a finite volume scheme of the incompressible Navier Stokes equation
TLDR
This paper proposes the classical Patankar scheme based on pressure correction, which is called Semi-Implicit Method for Pressure-Linked Equation (SIMPLE), which was tested on magnetic resonance images of the human brain and hands and compared with the classical implementation of the fluid image registration.
A Genetic Algorithm for Fully Automatic Non-Isometric Shape Matching
TLDR
The main observation is that optimizing an objective based on an induced dense functional correspondence, combined with geometric genetic operators, is highly effective for non isometric shape matching.
ENIGMA: evolutionary non-isometric geometry MAtching
TLDR
A fully automatic method for shape correspondence that is widely applicable, and especially effective for non isometric shapes and shapes of different topology, and which outperforms state of the art methods for automatic shape correspondence both quantitatively and qualitatively on challenging datasets.
Regularization with metric double integrals for vector tomography
Abstract We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space,…
A lattice Boltzmann method applied to the fluid image registration
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